An approach for robust matrix root-clustering analysis in a union of regions

On some relaxations commonly used in the study of linear systems

“…The first comment is that this robust Hurwitz stability test can be easily extended to many other performances tests such as H ∞ level [1], pole clustering constraints in convex regions i. e. D-stability [8,17,32] or even pole clustering constraints in non convex regions [3,4,5]. Indeed, all those performances have been expressed in terms of inequalities such as (1) or (54).…”

“…However, due to its simplicity, it remains very popular in the control community. The projection lemma, also called matrix elimination lemma DOI: 10.14736/kyb-2015-5-0830 [1,6,39] is particularly useful to synthesize some controllers [1,2,10] or to analyse the robustness of uncertain linear models with respect to polytopic uncertainties, through the notion of parameter-dependent Lyapunov functions [5,10,17,32]. It is also very popular in the control community.…”

Non-iterative pole placement technique: A step further

“…The solution provided by Algorithm 1 can be seen as a first step to initialize an optimization procedure dedicated to the derivation a robust non-strict but nonetheless precise pole placement control law (for example maximizing a criterion as the one presented in [26]). …”

Stability of LTI Systems with Unstructured Uncertainty Using Quadratic Disc Criterion

“…In practice, it is quite common that the uncertainties are given as a disturbance system whose elements in a disturbance matrix are not known exactly but only the bounds of the matrix are known [3]. Under this situation, many researches have been devoted to assigning the poles perturbed by the disturbance system into a desired region on the complex plane, which are known as D-stability or root clustering [1,7,11,12]. These methods depend on the solutions of algebraic matrix equations such as Riccati equation and Lyapunov equation.…”